I believe this approximation comes about by expressing the delay and the rise
time of a system functions of the "moments" of the impulse response. When you
do this, the delay and rise time can be found from derivatives of the frequency
response... or the first couple of terms in a series expansion of the frequency
response around w=0.

Then... the *magnitude* of the frequency response is expressible as a series in
w^2, since it is an even function. The expansion looks like

When two networks are cascaded, their magnitude functions are multiplied, and
the series expansion of the result is A01*A02 * ( 1 - (tr1^2 +tr2^2)/(4+pi) +
......) .

So, total rise time = sqrt of sum of squares of component rise times.

I believe this approximation works well for linear systems without overshoot. I
don't have a reference for this, although
the relation of rise time and the series expansion of the frequency response is
talked about in "Signal Analysis" by A. Papoulis on page 107.

Basically, this spec uses a "square root of the sum of the squares" type of
calculation, where, first, the RTD of a test fixture is measured. The
connector or whatever DUT is then inserted into the fixture, and the RTD of
this combination is measured. The RTD of the DUT is then calculated from
these two measurements using the sum of squares method.

Does anyone know where this method originated? I have seen a few references
that refer to it as a rule of thumb type calculation for cascading RTD's of
various devices. I have also seen a basic mathematical justification for it
in relation to oscilloscope bandwidths/risetimes. But in that case, it was
assumed that the devices being cascaded where R-C type networks. And even
then, I believe they said it was an approximation.

Not that I want to question the technical reasoning of the EIA or anything,
but does anyone out there have an opinion on how accurate this method might
be when applied to interconnects? Or might someone possibly even have a
mathmatical/physical justification for this method?

Thanks for any help anyone might offer.

Julian Ferry
Samtec, Inc.

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